Difference between 町 and 市?

The legal status of a municipality in any given country is going to be defined by things that the average person does not consider when they talk about if something is a city or a town.

I don’t think we’re talking about the proper names here, which are handled for you by the names themselves. We’re talking about using these in conversation.

It’s fine to call Tokyo a 町 in conversation (the use of which in that case would obviously be emphasizing the elements of “town-ness” even though Tokyo is something everyone knows is a city), even though it’s a 都 in law.

At the same time, it would be very strange to call some random inaka village a city in a sincere way.